Softbank agreed to pay $20.1 billion to acquire about a 70 percent stake in Sprint Nextel, as Japan’s third-biggest mobile-phone operator seeks growth overseas amid a declining local market. (Kiyoshi Ota/Bloomberg News)

In the priciest-ever overseas acquisition for a Japanese company, Softbank Corp. on Monday announced that it would buy about 70 percent of Sprint Nextel Corp., giving the U.S. carrier a much-needed cash infusion and boosting its chances to challenge giants Verizon and AT&T.

The $20.1 billion deal links a struggling U.S. mobile company, still trying to build up its high-speed next-generation network, with a Japanese wireless carrier noted for its history of risky — though so far fruitful — acquisitions.

In a joint press conference Monday with Sprint CEO Dan Hesse, Softbank’s billionaire founder Masayoshi Son said it was imperative to push overseas at a time when Japan’s own market, with its population declining and its economy stagnant, leaves little chance for growth. Softbank has a net debt of about $10 billion and it needed several major loans to finance the deal, but the strong yen gives the company greater purchasing power. The corporation’s stock plummeted in recent days after rumors of the deal leaked.

“When we make a challenge, usually risk comes along with it,” Son said. “I know it’s not an easy path to go business-wise.” But then Son noted Japan’s low birthrate and added, “However, without challenges [into new markets] we may face even bigger risks.”

The acquisition must still win approval from the U.S. Justice Department and the Federal Communications Commission. Sprint must convince the FCC that the deal is in the public interest to overcome a 25 percent limit on foreign investment in telecommunication companies.

Sprint, the nation’s third-largest wireless carrier, likely will argue that the proposal would increase competition in the United States and help it compete more effectively with Verizon and AT&T. Those two companies both have roughly twice the subscribers that Sprint does, and Sprint so far has struggled to break the duopoly.

Sprint, now a consolidated subsidiary of Softbank, has a net debt of about $15 billion after a half-decade of losses. At the Monday press conference, Hesse admitted the company was in shambles — at one point losing one million customers every quarter — when he became its top executive in 2007.

With its pockets drained, Sprint also held back on investment and left its customers on two separate networks. Now, Hesse said, Sprint is ready for what he called the “investment phase,” with the creation of a 4G network and improvements to the 3G network.

“We’re building a world-class platform,” Hesse said.

To acquire its share of Sprint, Softbank is buying up $12.1 billion in existing shares, at $7.30 per share. Sprint is also issuing $8 billion in new shares, which Softbank will buy at $5.25 per share.

Pushed together, Sprint and Softbank have 96 million customers. That makes Softbank the world’s third-largest mobile operator, behind China Mobile and Verizon.

Son said that he sees the potential for growth in the U.S. market and believes SoftBank can improve the “unbearable” network speeds in the United States.

Son praised Hesse’s leadership at Sprint and said that SoftBank’s investment and company history will accelerate the firm’s turnaround.

“This is a company that will turn around very quickly from here on,” Son said.